'Neo' Wiccans? Wicca was developed in the 20th Century. You don't get much more new than that as far as religions are concerned. That said, in this very, very short time different sects of Wicca have forked from the original. If you want to follow Wicca, being initiated into a coven and all, then the answer is that is depends. If you want to be a solitary practitioner or join a nom-traditional coven, then the answer is up to you.

I do not follow Wicca, and have not studied it. So I cannot give a lot of insight. But be aware that there are some who, if you are not initiated into a Gardnerian coven, will scathingly tell you that you are not Wiccan. Others will disagree on that point.

Prsona like you said, you dont know much about wicca and neo-wicca is certainly a thing. Even ask lark she is a high priestess of her own coven. Neo wicca was gennerally brought from people who arnt intiated into real traditional wiccan covens. Most are eclectic, like me.

1. 'Neo' as far as I'm aware means 'extreme' like 'Neo-Pagan' [aka Wicca] so unless you feel the title 'Neo-Wiccan' describes you, you don't have to use it [same goes for any title really] Wicca is a religion worshipping a God and Goddess, there are Wiccan paths that worship just the Goddess, or the God, and even some that worship neither deity but nature itself. There's nothing wrong with these paths but by the textbook definition it's not Wicca. It's not wrong or bad, just not Wicca.

2. Well yes and no. I think the Horned God being associated with the sun is a newer concepts [but I follow that belief so I'm not one to point fingers] Wiccans traditionally do worship a Triple Goddess [maiden, mother and crone and represented by the moon's phases] and a Horned God [please note he has antlers not devil horns] who is the ruler of the forest. His death and rebirth can be charted with the sun. Most Wiccans worship them, but many worship other deities or deities with similarities. [The Morigan, Isis, Pan, Osirus, so on] and again, it's not technically the Wicca Gerald Gardner founded, but Wicca does typically bend [it would be considered 'Eclectic Wicca']

3. If I understand your question correctly yes. If you feel drawn to or connected with another deity you can still follow Wiccan philosophies and worship them. [It just might get complicated if you worship a god of war or something]

Neo merely means new. But triple Deities have been worshipped for thousands of years. From the Egyptian Isis, Osiris,and Horus to the Christian Father,Son, and Holy Ghost.
The "new" religion of Wicca encompasses very old traditions; much older than Wicca! The old traditions had the Horned God (Earth), the Goddess (Moon), and the Creator (the Sun). Triple Deities.

If you aren't part of a particular Tradition of Wicca that honors specific Deities then you can build a relationship with any Gods and Goddesses to whom you feel drawn. Such do not have to be Gods or goddesses of the sun and moon. Nor do they have to have triple aspects. As an example, in my personal practice I work with Sekhmet, Anubis, and Thoth.

While there have been triple Goddesses in ancient religions it is important to remember that such Goddesses do not fall into the Maiden, Mother, Crone archetype of the Wiccan Goddess. You should not try to force ancient Goddess into the modern archetype where they nevr belonged.

"Egyptian Isis, Osiris,and Horus" are not a triple aspected deity such as the Father, Son, and Holy Spirit/Ghost of Christianity. Never have been, never will be. Heru/Horus who is Heru-sa-Aset or Horus, son of Isis, can be syncretized, via Shu/Heru-Shu with his father, Wesir/Osiris. However this does not mean that Heru-sa-Aset is Wesir, anymore than Heru-wer is Wesir or Heru-sa-Aset is Heru-wer. It's a way of representing the passage of kingship from father to son, which is the only time Heru-sa-Aset and Wesir are syncretized. However, synconization happens when one brings together two separate parts as opposed to having two sides or views of the same object (aspect).

Please Brysing, research Egyptian history and religion before you make a blanket statement based on New Age/New Age Christian theories that Heru-sa-Aset is Jesus, Wesir is God, and the Holy Ghost and/or Mary is Aset.